Finite element, least squares and domains decomposition methods for the numerical solution of nonlinear problems in fluid dynamics

Attention is given to fluid dynamics-related methods developed in recent years, some of which are of industrial interest; typically, these methods employ finite element approximations in order to handle complex geometries and nonlinear least squares formulations to treat nonlinearities. Conjugate gradient methods with scaling then solve the least squares problems, and subdomain decomposition is applied to reduce the solution of very large problems to that of problems of the same type but smaller domains. This decomposition approach allows the use of vector processors. Application of these methods to transonic flow calculations, to the numerical solution of the time-dependent Navier-Stokes equations for incompressible viscous fluids, and in the numerical solution of partial differential equation problems by domain decomposition, are presently noted.